Solutions Manual for
b b b
Design and Analysis of
b b b b
Experiments, 10e Doub b
glasMontgomery (All
b b b
Chapters)
, SolutionsbfrombMontgomery,bD.bC.b(2019)bDesignbandbAnalysisbofbExperiments,bWiley,bNY
Chapter 1 I b b
ntroduction b
Solutions
1.1S.b Supposebthatbyoubwantbtobdesignbanbexperimentbtobstudybthebproportionbofbunpoppedbkernelsbofbpopco
rn.b Completebstepsb1-
3bofbthebguidelinesbforbdesigningbexperimentsbinbSectionb1.4.b Arebtherebanybmajorbsourcesbofbvariationbthatbw
ouldbbebdifficultbtobcontrol?
Stepb1b–bRecognitionbofbandbstatementbofbthebproblem.b Possiblebproblembstatementbwouldbbeb–
bfindbthebbestbcombinationbofbinputsbthatbmaximizes byield bonbpopcornb–bminimize bunpoppedbkernels.
Stepb2b–
bSelectionbofbthebresponse bvariable.b Possiblebresponsesbarebnumber bofbunpoppedbkernelsbperb100bkernalsbinb
experiment,bweightbofbunpoppedbkernelsbversusbthebtotalbweightbofbkernelsbcooked.
Stepb3b–
bChoice bofbfactors, blevelsbandbrange. b Possible bfactorsbandblevelsbarebbrand bofbpopcornb(levels:bcheap,bexpensi
ve),bagebofbpopcornb(levels:bfresh,bold),btypebofbcookingbmethodb(levels:bstovetop,bmicrowave),btemperatureb
(levels:b150C,b250C),bcookingbtimeb(levels:b3bminutes,b5bminutes),bamountbofbcookingboilb(levels,b1boz,b3boz),b
etc.
1.2. Supposebthatbyoubwantbtobinvestigatebthebfactorsbthatbpotentiallybaffectbcookedbrice.
(a) Whatbwouldbyoubusebasbabresponsebvariablebinbthisbexperiment?b Howbwouldbyoubmeasurebtheb
response?
(b) Listballbofbthebpotentialbsourcesbofbvariabilitybthatbcouldbimpactbthebresponse.
(c) CompletebthebfirstbthreebstepsbofbthebguidelinesbforbdesigningbexperimentsbinbSectionb1.4.
Stepb1b–
Recognitionbofbandbstatementbofbthebproblem.bStepb2b–
b
bSelectionbofbthebresponsebvariable.
Stepb3b–bChoicebofbfactors,blevelsbandbrange.
1.3. Supposebthatbyoubwantbtobcomparebthebgrowthbofbgardenbflowersbwithbdifferentbconditionsbof
bsunlight, bwater, bfertilizer band bsoilbconditions. b Complete bstepsb1-
3bofbthebguidelinesbforbdesigningbexperimentsbinbSectionb1.4.
Stepb1b–
Recognitionbofbandbstatementbofbthebproblem.bStepb2b–
b
bSelectionbofbthebresponsebvariable.
Stepb3b–bChoicebofbfactors,blevelsbandbrange.
1-1
, SolutionsbfrombMontgomery,bD.bC.b(2019)bDesignbandbAnalysisbofbExperiments,bWiley,bNY
1.4. Selectbanbexperimentbofbinterestbtobyou.b Completebstepsb1-
3bofbthebguidelinesbforbdesigningbexperimentsbinbSectionb1.4.
1-2
, SolutionsbfrombMontgomery,bD.bC.b(2019)bDesignbandbAnalysisbofbExperiments,bWiley,bNY
1.5. SearchbthebWorldbWidebWebbforbinformationbaboutbSirbRonaldbA.bFisherbandbhisbworkbon
bexperimental bdesignbinbagricultural bscience batbthebRothamstedbExperimental bStation.
Samplebsearchesbcouldbincludebthebfollowing:
1.6. FindbabWebbSitebforbabbusinessbthatbyoubarebinterestedbin.b Developbablistbofbfactorsbthatbyoubwouldb
usebinbanbexperimentalbdesignbtobimprovebthebeffectivenessbofbthisbWebbSite.
1.7. Almostbeveryonebisbconcernedbaboutbthebrisingbpricebofbgasoline.b Constructbabcausebandbeffectbdia
grambidentifyingbthebfactorsbthatbpotentiallybinfluencebthebgasolinebmileagebthatbyoubgetbinbyourbcar.bHowb
wouldbyoubgobaboutbconductingbanbexperimentbtobdeterminebanybofbthesebfactorsbactuallybaffectbyourbgasol
inebmileage?
1.8. Whatbisbreplication?b Whybdobwebneedbreplicationbinbanbexperiment?b Presentbanbexamplebthatb
illustratesbthebdifferencesbbetweenbreplicationbandbrepeatedbmeasures.
Repetitionbofbthebexperimentalbruns.b Replicationbenablesbthebexperimenterbtobestimatebthebexperimentalberr
or,bandbprovidesbmorebprecisebestimatebofbthebmeanbforbthebresponsebvariable.
1.9 S.b Whybisbrandomizationbimportantbinbanbexperiment?
Tobassurebthebobservations,borberrors,barebindependentlybdistributedbrandomebvariablesbasbrequiredbbybstatist
icalbmethods.b Also,btob“averagebout”bthebeffectsbofbextraneousbfactorsbthatbmightboccurbwhilebrunningbthebex
periment.
1.10 S.bWhatbarebthebpotentialbrisksbofbabsingle,blarge,bcomprehensivebexperimentbinbcontrastbtobabsequential
approach?
b
Thebimportantbfactorsbandblevelsbarebnotbalwaysbknownbatbthebbeginningbofbthebexperimentalbprocess.b Evenb
newbresponsebvariablesbmightbbebdiscoveredbduringbthebexperimentalbprocess.b Bybrunningbablargebcompreh
ensivebexperiment,bvaluablebinformationblearnedbearlybinbthebexperimentalbprocessbcanbnotblikelybbebincorp
oratedbinbthebremainingbexperimentalbruns.
1-3
b b b
Design and Analysis of
b b b b
Experiments, 10e Doub b
glasMontgomery (All
b b b
Chapters)
, SolutionsbfrombMontgomery,bD.bC.b(2019)bDesignbandbAnalysisbofbExperiments,bWiley,bNY
Chapter 1 I b b
ntroduction b
Solutions
1.1S.b Supposebthatbyoubwantbtobdesignbanbexperimentbtobstudybthebproportionbofbunpoppedbkernelsbofbpopco
rn.b Completebstepsb1-
3bofbthebguidelinesbforbdesigningbexperimentsbinbSectionb1.4.b Arebtherebanybmajorbsourcesbofbvariationbthatbw
ouldbbebdifficultbtobcontrol?
Stepb1b–bRecognitionbofbandbstatementbofbthebproblem.b Possiblebproblembstatementbwouldbbeb–
bfindbthebbestbcombinationbofbinputsbthatbmaximizes byield bonbpopcornb–bminimize bunpoppedbkernels.
Stepb2b–
bSelectionbofbthebresponse bvariable.b Possiblebresponsesbarebnumber bofbunpoppedbkernelsbperb100bkernalsbinb
experiment,bweightbofbunpoppedbkernelsbversusbthebtotalbweightbofbkernelsbcooked.
Stepb3b–
bChoice bofbfactors, blevelsbandbrange. b Possible bfactorsbandblevelsbarebbrand bofbpopcornb(levels:bcheap,bexpensi
ve),bagebofbpopcornb(levels:bfresh,bold),btypebofbcookingbmethodb(levels:bstovetop,bmicrowave),btemperatureb
(levels:b150C,b250C),bcookingbtimeb(levels:b3bminutes,b5bminutes),bamountbofbcookingboilb(levels,b1boz,b3boz),b
etc.
1.2. Supposebthatbyoubwantbtobinvestigatebthebfactorsbthatbpotentiallybaffectbcookedbrice.
(a) Whatbwouldbyoubusebasbabresponsebvariablebinbthisbexperiment?b Howbwouldbyoubmeasurebtheb
response?
(b) Listballbofbthebpotentialbsourcesbofbvariabilitybthatbcouldbimpactbthebresponse.
(c) CompletebthebfirstbthreebstepsbofbthebguidelinesbforbdesigningbexperimentsbinbSectionb1.4.
Stepb1b–
Recognitionbofbandbstatementbofbthebproblem.bStepb2b–
b
bSelectionbofbthebresponsebvariable.
Stepb3b–bChoicebofbfactors,blevelsbandbrange.
1.3. Supposebthatbyoubwantbtobcomparebthebgrowthbofbgardenbflowersbwithbdifferentbconditionsbof
bsunlight, bwater, bfertilizer band bsoilbconditions. b Complete bstepsb1-
3bofbthebguidelinesbforbdesigningbexperimentsbinbSectionb1.4.
Stepb1b–
Recognitionbofbandbstatementbofbthebproblem.bStepb2b–
b
bSelectionbofbthebresponsebvariable.
Stepb3b–bChoicebofbfactors,blevelsbandbrange.
1-1
, SolutionsbfrombMontgomery,bD.bC.b(2019)bDesignbandbAnalysisbofbExperiments,bWiley,bNY
1.4. Selectbanbexperimentbofbinterestbtobyou.b Completebstepsb1-
3bofbthebguidelinesbforbdesigningbexperimentsbinbSectionb1.4.
1-2
, SolutionsbfrombMontgomery,bD.bC.b(2019)bDesignbandbAnalysisbofbExperiments,bWiley,bNY
1.5. SearchbthebWorldbWidebWebbforbinformationbaboutbSirbRonaldbA.bFisherbandbhisbworkbon
bexperimental bdesignbinbagricultural bscience batbthebRothamstedbExperimental bStation.
Samplebsearchesbcouldbincludebthebfollowing:
1.6. FindbabWebbSitebforbabbusinessbthatbyoubarebinterestedbin.b Developbablistbofbfactorsbthatbyoubwouldb
usebinbanbexperimentalbdesignbtobimprovebthebeffectivenessbofbthisbWebbSite.
1.7. Almostbeveryonebisbconcernedbaboutbthebrisingbpricebofbgasoline.b Constructbabcausebandbeffectbdia
grambidentifyingbthebfactorsbthatbpotentiallybinfluencebthebgasolinebmileagebthatbyoubgetbinbyourbcar.bHowb
wouldbyoubgobaboutbconductingbanbexperimentbtobdeterminebanybofbthesebfactorsbactuallybaffectbyourbgasol
inebmileage?
1.8. Whatbisbreplication?b Whybdobwebneedbreplicationbinbanbexperiment?b Presentbanbexamplebthatb
illustratesbthebdifferencesbbetweenbreplicationbandbrepeatedbmeasures.
Repetitionbofbthebexperimentalbruns.b Replicationbenablesbthebexperimenterbtobestimatebthebexperimentalberr
or,bandbprovidesbmorebprecisebestimatebofbthebmeanbforbthebresponsebvariable.
1.9 S.b Whybisbrandomizationbimportantbinbanbexperiment?
Tobassurebthebobservations,borberrors,barebindependentlybdistributedbrandomebvariablesbasbrequiredbbybstatist
icalbmethods.b Also,btob“averagebout”bthebeffectsbofbextraneousbfactorsbthatbmightboccurbwhilebrunningbthebex
periment.
1.10 S.bWhatbarebthebpotentialbrisksbofbabsingle,blarge,bcomprehensivebexperimentbinbcontrastbtobabsequential
approach?
b
Thebimportantbfactorsbandblevelsbarebnotbalwaysbknownbatbthebbeginningbofbthebexperimentalbprocess.b Evenb
newbresponsebvariablesbmightbbebdiscoveredbduringbthebexperimentalbprocess.b Bybrunningbablargebcompreh
ensivebexperiment,bvaluablebinformationblearnedbearlybinbthebexperimentalbprocessbcanbnotblikelybbebincorp
oratedbinbthebremainingbexperimentalbruns.
1-3
